The 2-torus attractor at F = 4 has singular values in the same range.
The resulting 2-torus attractor remains stable until F [approximately equal to] 3.791 and a 3-torus attractor appears.
We have shown that predictability of extremes increases near a saddle-node bifurcation of a periodic orbit but decreases near a saddle-node bifurcation of a 2-torus attractor.
In this case a 2-torus attractor disappears through a quasi-periodic saddle-node bifurcation which leads to a chaotic attractor.
A periodic attractor bifurcates into a 2-torus attractor at F [approximately equal to] 3.639 which in turn bifurcates into a 3-torus attractor at F [approximately equal to] 3.791.